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Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems
Univ Firenze, Italy.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. RUDN Univ, Russia.
2018 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 229, no 2, p. 569-599Article in journal (Refereed) Published
Abstract [en]

Best possible second-order regularity is established for solutions to p-Laplacian type equations with and a square-integrable right-hand side. Our results provide a nonlinear counterpart of the classical L (2)-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are obtained. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required, although our conclusions are new even for smooth domains. If the domain is convex, no regularity of its boundary is needed at all.

Place, publisher, year, edition, pages
SPRINGER , 2018. Vol. 229, no 2, p. 569-599
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-148359DOI: 10.1007/s00205-018-1223-7ISI: 000432698700003OAI: oai:DiVA.org:liu-148359DiVA, id: diva2:1219067
Note

Funding Agencies|Italian Ministry of University and Research (MIUR) [2012TC7588]; GNAMPA of the Italian INdAM - National Institute of High Mathematics; Ministry of Education and Science of the Russian Federation [02.a03.21.0008]

Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2018-07-03

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